NEW YORK – Naomi Osaka looked across the net after ending Coco Gauff’s U.S. Open in the third round Saturday night and saw the tears welling in the 15-year-old’s eyes.

Osaka also saw a bit of herself in the kid she’d just beaten 6-3, 6-0.

So the tournament’s defending champion and No. 1 seed, who is only 21 herself, comforted Gauff with a hug and words of consolation, then encouraged her to address the 23,000 or so folks in the Arthur Ashe Stadium stands who were pulling for the young American. Knowing how tough it is to lose, Osaka told her: “You need to let those people know how you feel.”

So Gauff obliged — a rare instance of a match’s loser addressing the crowd from the court. And was appreciative of Osaka’s gesture.

“She just proved that she’s a true athlete. For me, the definition of an athlete is someone who on the court treats you like your worst enemy, but off the court can be your best friend,” Gauff said later at her news conference. “I think that’s what she did tonight.”

Osaka got off to a quick start in the match, which lasted just 65 minutes.

“I’ve watched (Gauff) play a couple of times and I’ve always thought she was an incredible mover, so I thought I had to get going right off the bat,” Osaka said in her post-match interview.

Osaka held serve in the opening game with two aces and a pair of crisp backhand winners. She also nabbed the first break, as Gauff committed a game-ending double fault in the following game.

Gauff struggled with her serve throughout the match, but Osaka also found some difficulty as neither player managed to hold serve from the fifth through the eighth games of the set.

Osaka, who hit 24 winners in the match compared to eight by her opponent, let a few of her misses accumulate during this stretch, and also suffered a bit of bad luck when a key shot went out after striking the top of the net.

Still up a break at 5-3, however, Osaka held serve to take a one-set advantage.

From there, the Osaka native ran the table. After breaking her opponent in the first game of the second set, Osaka survived a triple-break threat in the following game.

She also relied on her powerful serve to hold at deuce in the fourth game, when her game-winning ace was called out but overturned after a challenge. Osaka had five aces in the match to two by Gauff.

The final game was a love hold for Osaka, who faces world No. 12 Belinda Bencic of Switzerland in the fourth round.

Osaka is the world’s top-ranked player, but Gauff has generated all sorts of attention already. She was the youngest woman since 1996 to win two matches at Flushing Meadows, her follow-up to a captivating run to the second week at Wimbledon in July.

In this much-hyped showdown under the lights, Gauff often looked exactly like what she is: an immensely talented player who is still learning her way at tennis’ top level.

“We definitely know what we’ve got to work on,” Gauff’s father, Corey, said. “She wanted to win the match. It wasn’t, ‘See how well you can do.’ “

Osaka’s advantages in age and accomplishments — she is a two-time major champion, including at the Australian Open in January — played a role. So, too, did her on-target power.

“For me, this is the most focused I’ve been since Australia,” said Osaka, who’s had an up-and-down season since earning that trophy and is wearing a black sleeve on her left knee, which has been problematic lately.

Addressing Gauff, she said: “I’m so sorry for playing you (with) this type of mentality.”

When it ended, Gauff began to bawl on the sideline. Osaka approached her and they spoke, briefly, then later cried, too, while addressing Gauff’s parents on-court.

“For me, it’s crazy to me to see how far she’s come in such a little amount of time,” said Osaka.

Both players are based in Florida now and have known each other for a few years. Their fathers are friends.

“She was crying; she won. I was crying. Everybody was crying,” Gauff said. “I was like, ‘You won the match!’ “

Moving into the men’s fourth round were three-time champion Rafael Nadal and 2014 title winner Marin Cilic, who are the only past Grand Slam champs in their half of the draw and now must face each other. Cilic, the No. 22 seed, overcame his own 17 double-faults and withstood 40 aces from 14th-seeded American John Isner to win 7-5, 3-6, 7-6 (8-6), 6-4.

Kyrgios is facing a possible suspension after calling the ATP “pretty corrupt” over a $113,000 fine it levied for outbursts at a tuneup tournament. He was relatively subdued Saturday, other than calling a line judge a “whistleblower” for reporting him to the chair umpire for cursing.

There’s always something with Kyrgios, who said afterward his eyes might have had trouble adjusting to the artificial lights in Ashe because he plays too many video games.